1. Field of Invention
The present invention relates to the technical field of microstructure characterization of crystalline materials and crystallographic analysis, and more particularly to a method for determining geometric relationships of crystal reciprocal vectors on the two-dimensional planes obtained from an EBSD (electron backscatter diffraction) pattern.
2. Description of Related Arts
Most of the currently used materials belong to crystalline materials. The conventional methods for determining an unknown crystal lattice comprise XRD (x-ray diffraction) and SAED (selected-area electron diffraction). These two classic methods have own advantages and disadvantages. The former has higher accuracy for analyzed unit cell parameters and is capable of applying the diffraction intensity to further precisely position atomic coordinates in unit cells. However, it is unable to directly observe microstructure morphology inside the sample in real time, and generally needs that the sample consists of single phase. The latter allows the user not only to use electron diffraction to characterize crystallography of the microstructure at regions of interest, but also to directly observe the morphology of the microstructure in real time on the transmission electron microscope, which is the greatest advantage. Its disadvantage is more difficult to prepare the sample. Therefore, it is still a challenging work to simultaneously characterize unknown crystal lattice and its morphology of a bulk sample in practice, and especially lacking a convenient, fast and accurate method to determine lattices with low symmetry which commonly exist in minerals.
In recent twenty years, the EBSD technique has made great progress in the aspect of materials science research. EBSD is an accessory of SEM (scanning electron microscope), so that microstructure morphology of crystalline materials are able to be directly observed in real time, thereby advantages of the SAED are kept. More importantly, the EBSD is used on the SEM, so that the requirements for preparing the sample are greatly simplified. Up to now, all applications of the EBSD technique have been limited on the basis of orientation analyses of known crystals. Therefore, it is no doubt that the function of determining unknown lattices of bulk crystals using an EBSD pattern provides a new operating mode for SEM. The present invention is beneficial to achieve such a new function.
In general, an EBSD pattern comprises dozens of Kikuchi bands, in which the width of each Kikuchi band is relevant to the interplanar spacing in a crystal. By means of the PC (pattern center) and the DD (detector distance) of an EBSD pattern, the length and direction of a reciprocal vector corresponding to a crystallographic plane in direct space can be determined via the width and azimuth of the Kikuchi band. The Kikuchi bands in an EBSD pattern intersect into different Kikuchi poles which are equivalent to two-dimensional reciprocal planes of the crystal. Generally, there are hundreds of Kikuchi poles in a single EBSD pattern, simultaneously providing hundreds of two-dimensional reciprocal planes of the crystal. Therefore, an EBSD pattern of a crystalline sample reflects rich crystallographic information, which is the greatest advantage of the EBSD technique. Compared with other diffraction techniques, disadvantages of the EBSD technique are poor contrasts at edges of the Kikuchi bands and large errors of measurement data, wherein the errors of the PC and the DD usually reach more than 10%, and the measurement errors of the width of the Kikuchi bands reach 20% (reference: D. J. Dingley and S. I. Wright. Determination of crystal phase from an electron backscatter diffraction pattern. J. Appl. Cryst. 42(2009):234-241).
In recent years, the applicants of the present application have disclosed the determination of Bravais lattice of unknown crystals by means of single EBSD pattern in references comprising: 3D reconstruction for Bravais lattice of unknown crystals using EBSD pattern. Journal of Chinese Electron Microscopy Society, December 2008, Vol. 27, No. 6; 3D reconstruction for Bravais lattice of hexagonal crystal using single EBSD pattern. Journal of Chinese Electron Microscopy Society, August 2010, Vol. 29, No. 4; Reconstruction for 3D reciprocal primitive cell of crystals using EBSD pattern. Paper collection of the second National Symposium on electron backscatter diffraction (EBSD) technology and application, the Sixth National Symposium on science and technology, Dec. 31, 2007; and Chinese patent application No. 200810237624.X, filed on Nov. 25, 2008, Method for determining Bravais lattice of unknown crystals using electron backscatter diffraction.
According to the above published references, the applicants disclosed the determination of Bravais lattice of unknown crystals based on a single EBSD pattern, which means using a large amount of two-dimensional reciprocal planes revealed from a single EBSD pattern, reconstructing a three-dimensional reciprocal lattice according to the geometric relationships of crystal reciprocal vectors on the two-dimensional planes, transforming the reciprocal lattice into a direct lattice. Before the three-dimensional reconstruction, every two-dimensional reciprocal plane needs to be determined from the EBSD pattern, and especially, the geometric relationships of crystal reciprocal vectors on the two-dimensional reciprocal planes need to be correctly described. Therefore, the correct geometric relationships are the key to achieve the three-dimensional reconstruction. However, due to large errors of EBSD original measurement data, even after geometric correction and a least squares fitting, the vector distributions on the two-dimensional reciprocal planes are still unable to directly reflect inherent geometric relationships.
Aiming at the shortcomings of the published methods, the present invention is provided.